Explain how liquefaction can occur in different steps within the same phase using an example.

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(N/A) Liquefaction of a gas can occur without passing through the two-phase (liquid + gas) region if the process is carried out above the critical temperature. This is demonstrated using the $CO_2$ isotherm diagram:
Step-$i$ (Point $A$ to Point $F$): We move from point $A$ to $F$ by increasing the temperature at constant volume,which also increases the pressure.
Step-$ii$ (Point $F$ to Point $G$): We compress the gas at a constant temperature along the isotherm (above the critical temperature,e.g.,$31.1^{\circ}C$). The pressure increases as the volume decreases.
Step-$iii$ (Point $G$ to Point $D$): We move vertically down from $G$ to $D$ by lowering the temperature. As we cross the critical isotherm,the substance transitions into the liquid state without ever entering the heterogeneous two-phase region.
In this series of changes,the substance remains in a single phase throughout the process.

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